10.3.4 Practice: Modeling: Factoring ax2 + bx + c Your Assignment: Patio Project
You have a small patio and want to improve it with a project. Circle the project you picked:
Fish Pond
Planter Box
Fire Pit

Making Sense of the Problem

Make Sense of the Problem (3 points: 1 point for each answer)
What do you know?

What do you want to find out?

What kind of answer do you expect?

Writing an Equation
1. Set your polynomial equal to the total area of your patio to create the equation. (1 point)

Getting the Right Side of the Equation Equal to 0
2. Use inverse operations to make the right side of the equation equal to 0. (2 points)

Factoring the GCF out of the Polynomial
3. Factor the GCF out of the trinomial on the left side of the equation. (2 points: 1 for the GCF, 1 for the trinomial)

Factoring the Polynomial Completely
4. Factor the polynomial completely. (4 points: 2 points for each factor)

5. If a product is equal to zero, we know at least one of the factors must be zero. And the constant factor cannot be zero. So set each binomial factor equal to 0 and solve for x, the width of your project. (2 points: 1 point for each factor)

6. Check your work. Substitute the two values of x into the equation from question 2 to confirm that it equals zero. (2 points: 1 point for each value of x)

7. What are the dimensions of your project? Remember that the width of your project is represented by x. (2 points: 1 point for each dimension)

Width =

Length =

8. Draw a new picture of your patio that shows the dimensions of your project and the border. (2 points) Check to confirm that the total area equals the area of your patio.